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dc.contributor.authorNestoridi, Evita
dc.contributor.authorOlesker-Taylor, Sam
dc.date.accessioned2022-01-28T16:36:21Z
dc.date.available2022-01-28T16:36:21Z
dc.date.issued2022-02
dc.date.submitted2020-07-15
dc.identifier.issn0178-8051
dc.identifier.others00440-021-01061-5
dc.identifier.other1061
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/333172
dc.description.abstract<jats:title>Abstract</jats:title><jats:p>In a recent breakthrough, Teyssier (Ann Probab 48(5):2323–2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to some famous problems: the <jats:italic>k</jats:italic>-cycle shuffle, sharpening results of Hough (Probab Theory Relat Fields 165(1–2):447–482, 2016) and Berestycki, Schramm and Zeitouni (Ann Probab 39(5):1815–1843, 2011), the Ehrenfest urn diffusion with many urns, sharpening results of Ceccherini-Silberstein, Scarabotti and Tolli  (J Math Sci 141(2):1182–1229, 2007), a Gibbs sampler, which is a fundamental tool in statistical physics, with Binomial prior and hypergeometric posterior, sharpening results of Diaconis, Khare and Saloff-Coste (Stat Sci 23(2):151–178, 2008).</jats:p>
dc.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectArticle
dc.subjectCutoff
dc.subjectLimit profiles
dc.subjectRandom walk on groups
dc.subjectSymmetric group
dc.subjectRepresentation theory
dc.subjectFourier transform
dc.subjectCharacters
dc.subjectGelfand pairs
dc.subjectHomogeneous spaces
dc.subjectSpherical functions
dc.subjectEigenvalues and eigenfunctions of Markov chains
dc.subjectSpectral representations
dc.subject20C15
dc.subject20C30
dc.subject43A30
dc.subject43A65
dc.subject43A90
dc.subject60B15
dc.subject60J10
dc.subject60J20
dc.titleLimit profiles for reversible Markov chains
dc.typeArticle
dc.date.updated2022-01-28T16:36:21Z
prism.endingPage188
prism.issueIdentifier1-2
prism.publicationNameProbability Theory and Related Fields
prism.startingPage157
prism.volume182
dc.identifier.doi10.17863/CAM.80595
dcterms.dateAccepted2021-04-29
rioxxterms.versionofrecord10.1007/s00440-021-01061-5
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidOlesker-Taylor, Sam [0000-0001-9764-1645]
dc.identifier.eissn1432-2064
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/R022615/1, Doctoral Training Grant 1885554)
cam.issuedOnline2021-07-14


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